They are usually the people who see a new QB come in and miss their first pass and yell "see he can't throw!" May not be able to but at least wait until you have a larger body of work from which to make that pronouncement.
What fans need to see is an upward trend or at least someone who is implementing a system everyone can get behind. Wins and losses should not really affect the new coach's first year perceptions - I said should not, not that it won't because people today want microwave results.
There will be those vocal ones who want the new coach gone halfway through the season - we should ignore them the way I tend to ignore several on here now. I doubt they will represent the majority.